The Ayalon prison near Tel Aviv where Prisoner X Ben Zygier took his own life after being secretly imprisoned. Photograph: Nir Elias/Reuters

The Israeli government has reportedly offered to pay hundreds of thousands of pounds in compensation to the family of "Prisoner X" – an agent of the Mossad with Australian and Israeli citizenship who took his own life while secretly imprisoned for undisclosed "grave charges".

An unnamed source was quoted in the Haaretz newspaper claiming a compensation deal was agreed six weeks ago following the conclusion of an official inquiry into the death of Ben Zygier, who was imprisoned in 2010 under a false identity and who killed himself in Unit 15, a "secret prison" within Ayalon jail near Tel Aviv.

Reports of a secret deal with the family follow claims by Zygier's lawyer that he had protested his innocence on the day before his death in a cell that was supposed to have been monitored 24 hours a day.

Its also comes amid mounting calls for the Mossad and the Israeli prison service to face investigation over their alleged negligence in the scandal. A justice ministry official said the judge who had originally handled the case has demanded a further inquiry "to examine issues of negligence".

"If she [the judge] had not found anything suspicious, she would not have transferred the case," said the official, adding that charges would be filed if the investigation finds there was any negligence in monitoring Zygier during his detention.

Neither Zygier's Israeli wife nor his Australian parents have spoken publicly about his detention or his death. His wife is believed to have fled her home in Israel owing to the unrelenting media interest in her late husband. The Prisoner X case, which was thrust into the international spotlight after an Australian documentary named Zygier earlier this week has prompted a furious debate in Israel over both its military censorship regime, which had tried to silence reporting about the case with draconian gagging orders, and the ability of Israel to "disappear" some prisoners.

As Israeli officials moved to say that Zygier was treated fairly, media in the country revealed that the case was not been unique and others suspected of security offences have been subjected to similar treatment. Several papers on Friday carried details of other 'Prisoner Xs', including Mordechai Kedar, a military intelligence officer who murdered a collaborator, KGB spies Marcus Klingberg and Shabtai Kalmanovich and Nahum Manbar.

According to one unnamed source familiar with the Zygier case who spoke the YNet website: "When an Israeli is detained for security offences, a process begins, but no one knows how it will end. He disappears into interrogation rooms, and no one knows where he is. They do it using two tools: A gag order and an injunction that prevents the detainee from meeting with an attorney.

"In this manner, the detainee is interrogated without being aware of his rights and without meeting anyone. The entire system is recruited to make him disappear."

Although it has not be revealed what crime Zygier was charged with, details about his life and the case have emerged in recent days, including a claim that he had been one of several Israelis with Australian passports who had worked for business exporting telecommunication equipment from Italy to Iran that was a cover for an espionage operation.

It has also been alleged that the Australian intelligence service Asio – which was already investigating the misuse of several Australian passports Zygier had acquired – believed he was about to disclose information about operations by the Mossad.

Zygier is known to have operated under several monikers, including Ben Alon. It was under this name that he visited Iran, Syria and Lebanon. The Age newspaper has also listed Benjamin Burrows as a name Zygier adopted while studying for an MBA at Monash University in Melbourne.

The latest claims came as Avigdor Feldman, a prominent human rights lawyer in Israel who visited Zygier in the days before his death to offer advice on the plea bargain he was negotiating, voiced his doubts over the official verdict of suicide.

Feldman told ABC: "I was impressed by a person thinking of his future and the decision he was about to make. I met someone who was definitely apprehensive, but with the rational apprehension of a person in his situation. The end of the affair is something that needs to be investigated."